As you have already experienced, it is possible and fairly common to develop under-eye edema from crying. The etiology of this occurrence is not completely clear, but it is likely due to increased water retention in the subcutaneous tissue in the thin under-eye skin due to salt in tears. Rarely, eye puffiness can be a sign of an underlying medical condition, so you should discuss this problem with your primary care doctor
Swelling or puffiness under the eyes is a common complaint and can be very frustrating. There are various causes including fluid retention from increased dietary salt intake, sleeping flat on your back, not getting enough sleep, and allergies. If you have a history of allergies or you eye edema is associated with redness, watering, or itching, then you should ask your primary care doctor about allergy medications and other possible therapies.
Depending on the cause of your under eye puffiness, therapies will differ. Since yours are due to crying and are not really preventable, you could try a cool compress. This can be done with a washcloth and cool water. Put the damp cloth under your eye for a few minutes with mild pressure. Cucumbers and cold tea bags are often suggested for the same cooling effect to help decrease the edema. There is some thought that caffeine may be useful, but this has not yet been proven. You should follow up with your primary care physician
to discuss your case and other possible causes and treatments.